1. Field of the Invention
The present invention relates to a method for determining the degree of symmetry and the azimuthal direction of any asymmetry in a circumferential gamma ray measurement. Still more particularly, the present invention relates to an algorithm for locating the azimuthal direction of any minimum or maximum value in a series of measurements that each represent a separate azimuthal sector, and for determining the azimuthal direction with a greater resolution and accuracy than the measuring device provides.
2. Background of the Invention
The recovery of subterranean hydrocarbons such as oil and gas often involves an substantial investment in drill rig structures and expensive drilling operations. In order to maximize the return on both of these expenditures, rig operators may utilize one or more horizontal well bores that branch from a single vertical well bore. For example, the vertical well bore may not be sufficiently close to hydrocarbon deposits to permit recovery. By drilling horizontally from a vertical well bore towards the hydrocarbon deposits, the need for multiple drilling rigs on the surface is eliminated. Moreover, where a vertical well bore has penetrated into a productive hydrocarbon deposit, a horizontal well bore can improve the drainage of hydrocarbons into the well bore.
Effective horizontal drilling is often accomplished by a steerable drilling assembly, such as are known in the art. When drilling horizontally, it is desirable to maintain the well bore in the pay zone, the formation containing hydrocarbons, as much as possible so as to maximize the recovery. However, pay zones may dip or vary in an unpredictable manner. Consequently, as a drilling assembly progresses through a pay zone, the drill bit may approach an adjacent nonproductive stratum. The pay zone and adjacent strata define bed boundaries within which the operator may wish to confine drilling activity. Effective "steering" of the drilling assembly so as to maintain the bore within the pay zone is possible only where the operator has information relating to subterranean geology and knowledge of parameters therein.
Recently, the industry has developed a variety of devices and techniques to collect data during the drilling process. By collecting and processing data during the drilling process, the operator can make accurate modifications or corrections without interrupting drilling, so as to optimize drilling operations. Devices for measuring conditions downhole and the movement and location of the drilling assembly contemporaneously with the drilling of the well have come to be known as "measurement-while-drilling" (MWD) techniques.
Gamma ray (GR) detectors are one type of tool that has been used in MWD operations and that can assist in maintaining a drilling assembly within the pay zone. Gamma rays have characteristic energy spectra that can be used to identify the substance of the source emitting the gamma rays. In passive gamma ray logging, naturally occurring radioactive isotopes, most commonly potassium, uranium and thorium, that are often present in a formation are the source of gamma rays sensed by such passive GR detectors. The incidence of gamma rays on the detectors, along with known information about the response of the tool, gives information about the source of the gamma rays, and thus gives information about the formation itself.
It is known in the art that an azimuthally focused tool can be used to collect gamma ray measurements. Such tools typically generate a series of count totals, where each total corresponds to an azimuthal orientation or the GR detector corresponding to a certain sector of the formation or the borehole. These tools usually comprise a single, rotating, azimuthally focused detector to scan the circumference of the well bore. Alternatively, such a tool can use two or more non-rotating detectors collecting data from complementary sectors of the formation, as disclosed in application Ser. No. 09/276,431, filed concurrently, entitled Radiation Detector and incorporated by reference in its entirety. Normally, gamma ray measurements in a particular pay zone are approximately azimuthally uniform because a pay zone consists mostly of one material, such as sand. Strata material such as shale and sand usually have reasonably unique gamma ray emission counts. As the drilling assembly nears a bed boundary, a directional GR detector will sense a variation in gamma ray measurements. Once the variation is detected and its azimuthal location is established, the operator can make corrections in accordance with known techniques to avoid exiting the pay zone. Thus, one method of maintaining a drilling path through the pay zone is to continually monitor gamma ray emissions proximate to the steerable drilling assembly.
Regardless of the type of tool that is used, the gamma ray count data will typically be in the form of a plurality of azimuthal sectors, for which the gamma ray counts have been totaled. Because the resolution of any answer that is based directly on these data is limited by the number of sectors into which the formation is divided, a method is desired that allows a more accurate determination of the azimuthal location of the variation without increasing tool complexity, size or cost.